37. Think About a Plan A quilter is making hexagonal placemats by sewing together six quilted isosceles triangles. Each triangle has a base length of 10 in. The function y = 5 tan θ y equals 5 tangent theta  models the height of the triangular quilts, where θ is the measure of one of the base angles. Graph the function. What is the area of the placemat if the triangles are equilateral?
    • How can a graph of the function help you find the height of each triangle?
    • How can you find the area of each triangle?
    • What will be the last step in your solution?
38. Ceramics An artist is making triangular ceramic tiles for a triangular patio. The patio will be an equilateral triangle with base 18 ft and height 15.6 ft.
    1. Find the area of the patio in square feet.
    2. The artist uses tiles that are isosceles triangles with base 6 in. The function y = 3 tan θ y equals 3 tangent theta  models the height of the triangular tiles, where θ is the measure of one of the base angles. Graph the function. Find the height of the tile when θ = 30 ° theta equals 30 degrees  and when θ = 60 ° . theta equals 60 degrees .
    3. Find the area of one tile in square inches when θ = 30 ° theta equals 30 degrees  and when θ = 60 ° . theta equals 60 degrees .
    4. Find the number of tiles the patio will require if θ = 30 ° theta equals 30 degrees  and if θ = 60 ° . theta equals 60 degrees .

Use the function y = 200 tan x y equals 200 tangent x  on the interval 0 ° ≤ x ≤ 141 ° . 0 degrees less than or equal to x less than or equal to 141 degrees .  Complete each ordered pair. Round your answers to the nearest whole number.

39. ( 45 ° , □ ) open 45 degrees comma white square close
40. ( □ ° , 0 ) open white square degrees comma 0 close
41. ( □ ° , − 200 ) open white square degrees comma negative 200 close
42. ( 141 ° , □ ) open 141 degrees comma white square close
43. ( □ ° , 550 ) open white square degrees comma 550 close

Write an equation of a tangent function for each graph.

44. 
45. 
46. 
47. Construction An architect is designing a hexagonal gazebo. The floor is a hexagon made up of six isosceles triangles. The function y = 4 tan θ y equals 4 tangent theta  models the height of one triangle, where θ is the measure of one of the base angles and the base of the triangle is 8 ft long.
    1. Graph the function. Find the height of one triangle when θ = 60 ° . theta equals 60 degrees .
    2. Find the area of one triangle in square feet when θ = 60 ° . theta equals 60 degrees .
    3. Find the area of the gazebo floor in square feet when the triangles forming the hexagon are equilateral.

48. 

    1. The graph of y = 1 − cos   x sin   x y equals . fraction 1 minus cosine x , over sine x end fraction  suggests a tangent curve of the form y = a tan b x . y equals eh tangent b x .  Graph the function using the window [ − 3 π , 3 π ] left bracket negative 3 pi comma 3 pi right bracket  by [ − 4 , 4 ] . left bracket negative 4 comma 4 right bracket .
    2. What is the period of the curve? What is the value of a?
    3. Find the x-coordinate halfway between a removable discontinuity and the asymptote to its right. Find the corresponding y-coordinate.
    4. Find an equivalent function of the form y = a tan b x . y equals eh tangent b x .

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